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Consider the function: f(x) = 0.5x if 0<x<1 f(x) = 0.5 if 1<x<2 f(x) =1.5-0.5x if...

Consider the function:

f(x) = 0.5x if 0<x<1

f(x) = 0.5 if 1<x<2

f(x) =1.5-0.5x if 2<x<3

f(x) = 0 otherwise.

a. Show that this is a PDF.

b. Calculate P(x<2.5) and P(0.5<x<2).

c. Find the expected value and the median of this distribution.

Math   Statistics-And-Probability   
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